A peer-to-peer network, as opposed to a client-server network, is one made up of individual computers which communicate directly with each other instead of communicating through a centralized server. The benefits of peer-to-peer networks are increased censorship resistance and improved privacy, as there is no central authority to regulate what is transferred over the network.
Each individual computer on the network is known as a node. Nodes communicate with each other to send data, share computational resources and to break apart more complex tasks into manageable pieces. In Bitcoin, the concept of decentralization depends on this peer-to-peer architecture.
Bitcoin is a peer-to-peer network where each transaction is broadcast across the network to all connected peers. If there is a disagreement about whether a transaction is legitimate, each peer can vote on whether to accept the transaction. Votes are equally weighted for each peer, meaning more than 50% of the network must vote to reach a consensus before any decision is made. Legitimate transactions are confirmed then added to the blockchain, a ledger of all transactions which is stored by every node, making it highly tamper-resistant.